PP with different contents of maleic anhydride graft PP was selected as the matrix materials for the OFBG in this research. The properties of PP are shown in Table 1, and the properties of MA-G-PP (maleic anhydride graft polypropylene) are shown in Table 2. The sensing coefficients of strain and temperature of the OFBG are 1.2 pm/με and 10 pm/°C, respectively.

The rheology behaviors of seven kinds of PP with different contents of MA-G-PP were tested using the AR2000 rheometer produced by TA Instruments. It can be seen from Figure 1 that the apparent viscosity of melting PP is very sensitive to temperature. With the temperature raises from 180 °C to 260 °C, the viscosity decreases to about the 1/3 of the original value of each specimen. The higher the content of the MA-G-PP, the lower the viscosity is. For low levels of MA-G-PP content, such as 0%, 1% and 3%, the change of viscosity is not apparent. A sudden drop appears for the 5% content, while 7%, 10% and 15% show almost identical results as the former. The viscosity of the PP with 5% of MA-G-PP is much lower than that of the PP without MA-G-PP, as shown in Figure 1. Concerning both the viscosity and the degradation of PP, 220 °C is a proper operating temperature.

It can be seen in Figure 2 that melted PP with different contents of MA-G-PP is a typical non-Newtonian fluid, and the viscosity decreases as the shear rate ascends. Concerning both the rheology behavior and the mechanical performance, the PP with 5% content of MA-G-PP was chosen as the proper matrix in this research to package the bare OFBG.

The idea of the paralleled semi-extension rule based algorithm is as follows: firstly, the algorithm decomposes the maximum terms space of the clause set into several partial maximum terms spaces, which convert the SAT problem of the clause set into the SAT problem of the partial maximum terms spaces. If there is a certain partial maximum terms space that is satisfied, then the clause set is satisfied. If all the partial maximum terms spaces are unsatisfied, then the clause set is unsatisfied. In other words, the clause set is satisfied. In the following, the concept of the partial maximum terms space is discussed.

The internal force of PP and OFBG can be calculated as follows: (1) σ p = ε s p 1 + C E p + A p A f E fwhere: σ_p, E_P and A_p represent the internal stress, modulus and sectional area of PP matrix, respectively; ε_sp is the free shrinkage strain of PP matrix without any restraint. E_f and A_f refer to the modulus and sectional area of optical fiber, respectively, C is creep coefficient.

Considering the size of sensor designed in this study, σ_p should be very small, which is about 0.0832 Pa. The creep of the sensor should not be significant and the strain in the sensor can remain the same level as that in the concrete or asphalt pavement. Therefore, it can test the real strain changes.

According to the model given by Ou and Zhou [16], the strain transfer performance of the interface between the fiber and PP as shown in Figure 3 can also be expressed by the following equation: (2) λ 2 = 2 G PP E c r c 2 ln r PP r cwhere λ—strain transfer eigenvalue, E_c—modulus of OFBG, r_c—radius of OFBG, G_pp—shear modulus of the matrix, r_pp—radius of the matrix.

So, the error rate of the strain transfer of the interface between OFBG and matrix (η) and correction factor (k) can be described as: (3) η = ch ( λ l f ) − 1 λ l f sh ( λ l f ) (4) k = 1 1 − η

The shear modulus of PP ranges from 0.32 to 0.75 GPa, and the diameter of sensor is 5∼20 mm. E_c is about 70 GPa and r_c is about 6.25 × 10⁻² mm, the l_f is 10 mm. The relationship of η and G_pp and r_pp is shown in Figures 4 and 5, respectively.

With the G_pp (0.4 Gpa) and r_c (14 mm), the error rates of the strain transfer of the interface between OFBG and matrix (η) and correction factor (k) are 0.126898 and 1.145342, respectively, and the strain sensing coefficient is 1.04 pm/με.

The rate of extrusion for the PP based OFBG strain sensor is set as 16 r/min. The temperature settings of the extruder are shown in Table 3.

The fabrication process includes the following four steps as shown in Figure 6: (1) PP matrix is melted and extruded from the extruder; (2) Melted PP matrix enters a mould with a bare OFBG fixed along the axis; (3) The mould is put into a cooling water channel to harden the PP matrix; (4) Open the mould and the sensor is obtained. The PP-packaged OFBG strain sensor is as shown in Figure 7.

OFBG have been used for monitoring FRP or concrete inner strain changes during their hardening process, and valuable conclusion were obtained [17,18]. Thus, during the fabricating of the sensor, the inner strain and temperature changes of the PP matrix with the OFBG were monitored to ensure that the bare OFBG was bonding well with the PP matrix.

The temperature-time relationship of OFBG is shown in Figure 8. The extrusion temperature of PP was originally set at about 220 °C. After PP went inside the mould and reached the OFBG position, the temperature of PP became 152.57 °C and continued descending. This would increase the viscosity of PP and hence, the viscous force increases accordingly. Figure 9 shows the strain changes of the OFBG, and from which it can be seen that the shrinkage of PP is very large. By hardening for 50 minutes, the inner strain reached −12,000 με. Three days later, the wavelength was stable at about 1,524,320 nm, and the inner strain change was about −13,060 με, which truly reflected the shrinkage of PP. Because of the high ultimate strain of PP, this sensor maybe suitable to monitor large scale tensile strains.

Axial compressive test is performed to concrete column embedded with the proposed sensor to monitor strain under different load. In order to comparison, resistance strain gauges are also stuck on the lateral sides of the concrete column as shown in Figure 13. The test using load instrumentation were conducted obtain force of three load-unload cycle in elastic stage and the course to failure. The results are shown in Figure 14.

Figure 14(a) shows the strain curves of the developed sensor and resistance gauge. It can be seen that they are similar. Due to the high stiffness of resistance gauges, strain measured by them is a bit smaller. Three curves under three load-unload cycles in Figure 14(b) possess good repeatability and linearity. It can be verified that stickiness between optical fiber Bragg grating and polypropylene, sensor and concrete are all reliable. The whole response in Figure 14(c) correlatively tracks the course of load and strain. When the strain is less than 600 με, elastic deformation arises. When the strain reaches 1,200 με, failure occurs. Correlative curve between load and central wavelength of the developed sensor is shown in Figure 14(d). It is almost a straight line with a proportion coefficient of 4.35 pm/kN and correlative coefficient of 0.9999.

Steel dies with inner size of 100 mm × 100 mm × 400 mm were prepared. The new developed sensor is embedded after 10 mm thick asphalt concrete is spread. The following operation is the same as the fabrication of regular asphalt specimens. The MTS810 test machine is used to press the beam as shown in Figure 15. The load is from 0.5 KN∼5 KN, and the steps are 0.5 KN. Two displacement transducers are also installed to measure the flexibility of the beam. According to the monitoring results, we can see that the deformation of the asphalt specimen can be divided into two parts, recoverable and unrecoverable, as shown in Figure 16.

The strain changes of the asphalt specimen can be calculated according to the knowledge of materials mechanics: ε sensor = ε × y ( h 2 ) = 108 δ h 23 L 2 × 2 y h = 24 δ 23 a 2 ywhere: a = h = (1/3)L, y = (2/5)h=(2/15)L. And δ can be obtained by two methods. One is by MTS, and the other is by LVDT.

Measured and actual strains are drawn in Figure 17. From the results we can say that measured strain matches linearly with the actual one. The correlation coefficient was 0.9916, although maybe due to the position of the sensors in the specimens, the two fitted equations show a small difference.